Uniform deviation bounds limit the difference between a model’s expected loss and its loss on an empirical sample uniformly for all models in a learning problem. As such, they are a critical component to empirical risk minimization. In this paper, we provide a novel framework to obtain uniform deviation bounds for loss functions which are unbounded. In our main application, this allows us to ob...

Multi-attribute decision problems with uncertainty largely exist in the real world, it is very necessary to solve these problems. The paper proposes a grey correlation method based on maximizing deviation to solve the multiple attribute decision-making problems under risk in which the weight is unknown and attribute values are interval numbers. In the grey correlation method, according to diffe...

A single-camera, high-speed, polarization-sensitive, spectral-domain optical-coherence-tomography system was developed to measure the polarization properties of the in vivo human retina. A novel phase-unwrapping method in birefringent media is described to extract the total reflectivity, accumulative retardance, and fast-axis orientation from a specially designed sequence of polarization states...

The goal of the work described in this paper is to develop a very low bit rate vocoding scheme. The vocoder is a typical LPC vocoder, whose parameters are post-processed on a phone-byphone basis, resulting in a variable bit rate segment vocoder. Given the well known speaker recognizability problems presented by vocoders at such low bit rates, we have attempted to integrate a speaker modificatio...

In this paper we are concerned with the moderate deviation principle for the normalized partial sums process Wn, considered as an element of D([0, 1]) (functions on [0, 1] with left-hand limits and continuous from the right), equipped with the Skorohod topology (see Section 14 in Billingsley (1968) for the description of the topology on D([0, 1])). More exactly, we say that the family of random...

We investigate the local times of a continuous-time Markov chain on an arbitrary discrete state space. For fixed finite range of the Markov chain, we derive an explicit formula for the joint density of all local times on the range, at any fixed time. We use standard tools from the theory of stochastic processes and finite-dimensional complex calculus. We apply this formula in the following dire...

28 size spectra of extensive air showers in the knee region from 7 different experiment are analysed consistently. They are fitted by adjusting either 4 or 5 parameters: knee position, power law exponents above and below the knee region, overall intensity and, in addition, a parameter describing the smoothness of the bend. The residuals are then normalized to the same knee position and averaged...

The total ozone measurements by Belsk’s Dobson spectrophotometer have been compared with the satellite total ozone taken during the OMI (on board of Aura spacecraft) overpasses for the period August 2004 – July 2006. The agreement between both data sets is much better if the results of the recent (June 2005) calibration campaign of Belsk’s Dobson at Hohenpeissenberg are incorporated to the stan...

Background: To increase the effectiveness of orthodontic treatment in children with various degrees of dental enamel caries resistance using a personified orthodontic treatment. Materials and Methods: The present study included 108 adults (6-16 years old) with the first class of occlusion who referred for the Department of Pediatric Dent...

Deviation equation of Synge and Schild has been investigated over dif-ferentiable manifolds with contravariant and covariant affine connections (whose components differ not only by sign) and metric [(Ln, g)-spaces]. It is shown that the condition £ ξ u = 0 for obtaining this equation is only a sufficient (but not necessary) condition. By means of a non-isotropic (non-null) vector field u [g(u, ...